<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="trees_1.html#NM1">Tree</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:103"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="trees_2.html#K2">-level</a> 1 <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="trees_2.html#K2">-level</a> 1
 <b>and </b><br/><a NAME="E2:103"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>1</sub></font> <a href="trees_1.html#K4">|</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="trees_1.html#K4">|</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:103"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="103_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:103_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">c<sub>6</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:103_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="modal_1.html#T4">MODAL_1:4</a></i>;<br/><a NAME="E4:103_1"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="trees_2.html#K2">-level</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1 </span>}</span>  &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> as    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="trees_3.html#E3:103_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="trees_1.html#T46">TREES_1:46</a></i>;<br/><a NAME="E6:103_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="trees_2.html#K2">-level</a> 1
 <b>by </b><i><a class="txt" href="trees_3.html#E4:103_1"><i><font color="Green">E46</font></i></a></i>;<br/><a NAME="E7:103_1"/><b>then </b>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="trees_2.html#K2">-level</a> 1 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="trees_2.html#K2">-level</a> 1 <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="trees_3.html#E1:103"><i><font color="Green">E43</font></i></a></i>;<br/><a NAME="E8:103_1"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="trees_1.html#K4">|</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="trees_1.html#K4">|</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="trees_1.html#K4">|</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="trees_3.html#E2:103"><i><font color="Green">E44</font></i></a>, <a class="txt" href="trees_3.html#E3:103_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="trees_1.html#D9">TREES_1:def 9</a></i>;<br/><b>hence </b><a NAME="E9:103_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="trees_3.html#E3:103_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="trees_1.html#D9">TREES_1:def 9</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:103"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="trees_1.html#T47">TREES_1:47</a></i>;<br/>


</div>
